 
Summary: Short Eigenvectors and
Multidimensional Theta Functions
Ron M. Adin \Lambda
Department of Mathematics and Computer Science
BarIlan University
RamatGan 52900, ISRAEL
Email: radin@bimacs.cs.biu.ac.il
Yaacov Kopeliovich y
Department of Mathematics
University of California
Irvine, CA 92717
Email: ykopelio@math.uci.edu
Version of December 19, 1995
Abstract
A certain family of symmetric matrices, with entries \Sigma1, is known to determine
all the quartic relations that hold between multidimensional theta constants.
Attention is drawn here to combinatorial properties of the shortest possible
quartic relations, corresponding to vectors with minimal support in a certain
eigenspace of such a matrix. A lower bound for the size of the support is estab
lished, exhibiting a ``phase transition'' at dimension four. The multiplicityfree
